A077780 Numbers k such that (10^k - 1)/9 + 3*10^floor(k/2) is palindromic wing prime (a.k.a. near-repdigit palindromic prime).

5, 7, 65, 91, 3089, 299221

Offset

1,1

Comments

Prime versus probable prime status and proofs are given in the author's table.

References

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Table of n, a(n) for n=1..6.

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)

Makoto Kamada, Prime numbers of the form 11...11411...11

Index entries for primes involving repunits.

Formula

a(n) = 2*A107124(n) + 1.

Example

7 is a term because (10^7 - 1)/9 + 3*10^3 = 1114111.

Mathematica

Do[ If[ PrimeQ[(10^n + 27*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 3100, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Sequence in context: A378203 A177336 A108200 * A307361 A387760 A386196

Adjacent sequences: A077777 A077778 A077779 * A077781 A077782 A077783

Keyword

more,nonn,base,changed

Author

Patrick De Geest, Nov 16 2002

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018

a(6) from Robert Price, Jun 12 2026

Status

approved